Lock-step
In early multi-PC gaming, lock-step reigned as the only effective method of keeping players on a network synchronized. Every "tick" on the network, information was passed around until there was a consensus among all computers about where everything was and what it was doing. This didn't take very long and was not particularly noticeable, however it had a big problem: if a person with a fast computer played with a person with a slow computer: the fast computer was always waiting around for the slow computer to keep up. The players on the slower computers thus seemed to "skip" around whenever their position was updated on the network. Obviously, this annoyed the fast computer users.
Client-Server
Quake pioneered a technology which was slightly better than Lock Step- one machine was designated the 'server' and was the absolute authority. All of the other machines just told the server what the player on that end was doing, and the server dictated what happened and told the clients what to render as a result. This was effective but used rather a lot of bandwidth.